Second derivative free sixth order continuation method for solving nonlinear equations with applications

In this paper, we deal with the study of convergence analysis of modified parameter based family of second derivative free continuation method for solving nonlinear equations. We obtain the order of convergence is at least five and especially, for parameter \(\alpha =2\) sixth order convergence. Some application such as Max Planck’s conservative law, multi-factor effect are discussed and demonstrate the efficiency and performance of the new method (for \(\alpha =2\)). We compare the absolutely value of function at each iteration \(|f(x_n)|\) and \(|x_n-\xi |\) with our method and Potra and Pták method [1], Kou et al. method [2]. We observed that our method is more efficient than existing methods. Also, the Dynamics of the method are studied for a special case of the parameter in convergence.     

Mean-based iterative methods for finding multiple roots in nonlinear chemistry problems

Journal of Mathematical Chemistry - This research deals with the problem of finding multiple roots of nonlinear equations. Not long ago, Chicharro et al. have derived an efficient class of optimal...     

An efficient algorithm for solving nonlinear equations with a minimal number of trial vectors: applications to atomic-orbital based coupled-cluster theory

The conjugate residual with optimal trial vectors (CROP) algorithm is developed. In this algorithm, the optimal trial vectors of the iterations are used as basis vectors in the iterative subspace. For linear equations and nonlinear equations with a small-to-medium nonlinearity, the iterative subspace may be truncated to a three-dimensional subspace with no or little loss of convergence rate, and the norm of the residual decreases in each iteration. The efficiency of the algorithm is demonstrated by solving the equations of coupled-cluster theory with single and double excitations in the atomic orbital basis. By performing calculations on H(2)O with various bond lengths, the algorithm is tested for varying degrees of nonlinearity. In general, the CROP algorithm with a three-dimensional subspace exhibits fast and stable convergence and outperforms the standard direct inversion in iterative subspace method.     

Synthesis of chromophores and polyimides with a green chemistry approach for second‐order nonlinear optical applications

This article presents the synthesis of nonlinear optical responsive chromophores by adopting a green chemistry approach by coupling N‐methyl‐N‐(2‐hydroxyethyl)‐4‐amino benzaldehyde with barbituric acid, 1,3‐indanedione, and 1,3‐diethyl‐2‐thiobarbituric acid as the acceptors through stilbene linkage. We performed the synthesis in less than 10 minutes at room temperature with water as a solvent without catalyst. Two different side‐chain polyimides were synthesized from poly(hydroxy‐imide)s with chromophores by Mitsunobu reaction. The chromophores were characterized by Fourier transform infrared, ¹H NMR, ¹³C NMR, and elemental analysis. However, the polyimides were characterized by Fourier transform infrared and ¹H NMR. The inherent viscosities (η_inh) of polyimides were determined by Ubbelohde viscometer, which ranged between 0.1793 and 0.1890 dL/g. The molecular weights of the polyimides were determined using gel permeation chromatography and were in range of 23 000 to 26 000. Polyimides demonstrated an excellent solubility in polar aprotic solvents, indicating good processability. Thermal behavior of these polyimides was studied by differential scanning calorimetry and thermogravimetric analysis. The T_g's were in the range of 185°C to 255°C. The change in the molecular orientation in the polymer films after electrical poling was ascertained using ultraviolet‐visible spectrophotometer and atomic force microscopy. The thicknesses and refractive indices of the thin films were determined by an ellipsometer. The second harmonic generation coefficients of the corona‐poled polymer films at T_opt's, determined by the Maker fringe technique, ranged between 59.33 and 77.82 pm/V. High thermal endurance observed for the polyimides is attributed to the extensive hydrogen bonds in the matrix. The developed polyimides showed no decay in second harmonic generation signals below 110°C, indicating the acceptance for nonlinear optical devices.     

Organometallic chemistry related to applications for microelectronics in Japan

This is meant to be a brief overview of the developments of research activities in Japan on organometallic compounds related to their use in electronic and optoelectronic devices. The importance of organometallic compounds in the deposition of metal and semiconductor films for the fabrication of many electronic and opto-electronic devices cannot be exaggerated. Their scope has now extended to thin-film electronic ceramics and high-temperature oxide superconductors. A variety of organometallic compounds have been used as source materials in many types of processing procedures, such as metal–organic chemical vapor deposition (MOCVD), metalorganic vapor-phase epitaxy (MOVPE), metal–organic molecular-beam epitaxy (MOMBE), etc. Deposited materials include silicon, Group III–V and II–VI compound semiconductors, metals, superconducting oxides and other inorganic materials. Organometallic compounds are utilized as such in many electronic and optoelectronic devices; examples are conducting and semiconducting materials, photovoltaic, photochromic, electrochromic and nonlinear optical materials. This review consists of two parts: (I) research related to the fabrication of semiconductor, metal and inorganic materials; and (II) research related to the direct use of organometallic materials and basic fundamental research.     

A family of parametric schemes of arbitrary even order for solving nonlinear models: CMMSE2016

Many problems related to gas dynamics, heat transfer or chemical reactions are modeled by means of partial differential equations that usually are solved by using approximation techniques. When they are transformed in nonlinear systems of equations via a discretization process, this system is big-sized and high-order iterative methods are specially useful. In this paper, we construct a new family of parametric iterative methods with arbitrary even order, based on the extension of Ostrowski’ and Chun’s methods for solving nonlinear systems. Some elements of the proposed class are known methods meanwhile others are new schemes with good properties. Some numerical tests confirm the theoretical results and allow us to compare the numerical results obtained by applying new methods and known ones on academical examples. In addition, we apply one of our methods for approximating the solution of a heat conduction problem described by a parabolic partial differential equation.     

Graphene quantum dots from chemistry to applications

Graphene quantum dots (GQDs) have been widely studied in recent years due to its unique structure-related properties, such as optical, electrical and optoelectrical properties. GQDs are considered new kind of quantum dots (QDs), as they are chemically and physically stable because of its intrinsic inert carbon property. Furthermore, GQDs are environmentally friendly due to its non-toxic and biologically inert properties, which have attracted worldwide interests from academic and industry. In this review, a number of GQDs preparation methods, such as hydrothermal method, microwave-assisted hydrothermal method, soft-template method, liquid exfoliation method, metal-catalyzed method and electron beam lithography method etc., are summarized. Their structural, morphological, chemical composition, optical, electrical and optoelectrical properties have been characterized and studied. A variety of elemental dopant, such as nitrogen, sulphur, chlorine, fluorine and potassium etc., have been doped into GQDs to diversify the functions of the material. The control of its size and shape has been realized by means of preparation parameters, such as synthesis temperature, growth time, source concentration and catalyst etc. As far as energy level engineering is concerned, the elemental doping has shown an introduction of energy level in GQDs which may tune the optical, electrical and optoelectrical properties of the GQDs. The applications of GQDs in biological imaging, optoelectrical detectors, solar cells, light emitting diodes, fluorescent agent, photocatalysis, and lithium ion battery are described. GQD composites, having optimized contents and properties, are also discussed to extend the applications of GQDs. Basic physical and chemical parameters of GQDs are summarized by tables in this review, which will provide readers useful information.     

Improved semilocal convergence analysis in Banach space with applications to chemistry

We present a new semilocal convergence analysis for Secant methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost on the parameters involved our convergence criteria are weaker and the error bounds more precise than in earlier studies. A numerical example is also presented to illustrate the theoretical results obtained in this study.     

Automatic code generation for quantum chemistry applications

A unified, computer algebra system‐based scheme of code‐generation for computational quantum‐chemistry programs is presented. Generation of electron‐repulsion integrals and their derivatives as well as exchange‐correlation potential and its derivatives is discussed. Application to general‐purpose computing on graphics processing units is considered.     

Haar wavelet method for solving some nonlinear Parabolic equations

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In this paper, we develop an accurate and efficient Haar transform or Haar wavelet method for some of the well-known nonlinear parabolic partial differential equations. The equations include the Nowell-whitehead equation, Cahn-Allen equation, FitzHugh-Nagumo equation, Fisher’s equation, Burger’s equation and the Burgers-Fisher equation. The proposed scheme can be used to a wide class of nonlinear equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.     

Real molecules as models for mathematical chemistry

A [2]-catenane consisting of methylene groups and two additional acetylated aza groups has been synthesized in a multi-step sequence. After splitting off the acetyl bonds, the resulting secondary diamine should provide a good starting material for stepreaction (condensation or addition, respectively) polymerization.     

Relativistic free complement method for correctly solving the Dirac equation with the applications to hydrogen isoelectronic atoms

The accuracy of the relativistic free complement (FC) method, which was previously reported for solving the Dirac?CCoulomb equations of atoms and molecules, has been strictly examined with the applications to hydrogen isoelectronic atoms. The FC wave function grown up by the Hamiltonian automatically takes care of the correct relationship between large and small components, i.e., FC or ICI balance. Combining the FC method with the inverse Hamiltonian method can help to obtain correct solutions safely against to several obstacles characteristic to the Dirac?CCoulomb equation. To ensure the exactness of the obtained wave function, we examined the total square deviation from the exact wave function, local energy constancy, H-square error, and energy upper and lower bounds for hydrogen-like atoms.     

New improved convergence analysis for Newton-like methods with applications

We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases not covered in earlier studies. The advantages of our approach include, under the same computational cost as previous studies, a more precise convergence analysis under the same computational cost on the Lipschitz constants involved. Numerical studies including a chemical application are also provided in this study.     

Analytical chemistry of nonlinear systems

Analytical methods for characterizing complex, nonlinear chemical systems are reviewed. Emphasis is on those aspects of systems which make their characterization more difficult than just measuring concentrations or simple reaction rates. Examples include phase transitions, oscillating chemical reactions, laser fluctuations, and electrochemical oscillations. Data reduction algorithms specific to such systems are described.     

Surface chemistry of gold nanoparticles for health-related applications

Functionalization of gold nanoparticles is crucial for the effective utilization of these materials in health-related applications. Health-related applications of gold nanoparticles rely on the physical and chemical reactions between molecules and gold nanoparticles. Surface chemistry can precisely control and tailor the surface properties of gold nanoparticles to meet the needs of applications. Gold nanoparticles have unique physical and chemical properties, and have been used in a broad range of applications from prophylaxis to diagnosis and treatment. The surface chemistry of gold nanoparticles plays a crucial role in all of these applications. This minireview summarizes these applications from the perspective of surface chemistry and explores how surface chemistry improves and imparts new properties to gold nanoparticles for these applications.

Functionalization of gold nanoparticles is crucial for the effective utilization of these materials in health-related applications.     

Multiscale modeling and simulation methods with applications to dendritic polymers

Dendrimers and hyperbranched polymers represent a novel class of structurally controlled macromolecules derived from a branches-upon-branches structural motif. The synthetic procedures developed for dendrimer preparation permit nearly complete control over the critical molecular design parameters, such as size, shape, surface/interior chemistry, flexibility, and topology. Dendrimers are well defined, highly branched macromolecules that radiate from a central core and are synthesized through a stepwise, repetitive reaction sequence that guarantees complete shells for each generation, leading to polymers that are mono-disperse. This property of dendrimers makes it particularly natural to coarsen interactions in order to simulate dynamic processes occurring at larger length and longer time scales. In this paper, we describe methods to construct 3-dimensional molecular structures of dendrimers (Continuous Configuration Boltzmann Biased direct Monte Carlo, CCBB MC) and methods towards coarse graining dendrimer interactions (NEIMO and hierarchical NEIMO methods) and representation of solvent dendrimer interactions through continuum solvation theories, Poisson–Boltzmann (PB) and Surface Generalized Born (SGB) methods. We will describe applications to PAMAM, stimuli response hybrid star-dendrimer polymers, and supra molecular assemblies crystallizing to A15 colloidal structure or Pm6m liquid crystals.     

Some applications of thermal analysis to the coordination chemistry

The behaviour of complexes of the type MeD2I2 (Me=Co,D = acetylacetone or benzoylacetone,I = imidazole and derivatives in the course of the stepwise thermal degradation is different. In the case ofD = acetylacetone in the first step acetylacetone is split off. At D = benzoylacetone the decomposition starts with the partial elimination of the heterocyclic ligands.In-position unsubstituted nickelacyclic complexes from type (bipy)Ni(CH₂CH₂CH₂COO) decompose by a reductive elimination and separating of CO₂ forming a (bipy)Ni-intermediate. A single reductive decoupling is hindered by blocking up the-position.Opposite to the high thermal stability of the trimesityl aluminium the intermediates Almes₂Cl and AlmesCl₂ show with decreasing amounts of mesityl groups and increasing content of halogene, respectively, a significant decreasing thermal stability.The thermal degradation of nickelchelates of alkylsubstituted chinolin-8-ol starts with the dehydration followed by a different separation of the ligands as a function of the chain-length and the position of the substituents of the ligands.

---

Zusammenfassung Das Zersetzung Verhalten der Komplexverbindungen vom Typ C0D2I2 (P = acetylaceton, Benzoylaceton;I = Imidazol oder Derivate) erfolgt stufenweise. Im Falle vonD = Acetylaceton erfolgt zuerst eine Eliminierung von Acetylaceton wärend beiD = Benzoylaceton zuerst ein Heteroligand eine Abspaltung erfährt.Bei einer unsubstituierten-Position von Nickelacyclen des Typs (bipy)Ni(CH₂CH₂CH₂COO) erfolgt eine thermisch induzierte-Hydrideliminierung unter Ringspaltung und Freisetzung von CO₂.Im Gegensatz zur hohen thermischen Stabilität des Trimesityl Aluminium erfahren die Zwischenverbindungen Almes₂Cl und AlmesCl₂ mit abnehmenden Mesityl- bzw. zunehmenden Chlorgehalt einen wessentlich früheren thermischen Zerfall. Bei zunehmenden Kovalenzgrad ist hier ein Einfluss der veränderten Polarisation anzunehmen.Der thermische Abbau der prinzipiell wasserhaltig kristallisierenden Nickelchelate von alkylsubstituierten Chinolin-8-ol beginnt jeweils mit der Dehydratisierung. In Abhängigkeit von der Kettenlänge und der Position der Substitution am Chinolin schliesst sich der thermische Abbau der Chelatliganden ein- bzw. mehrstufig an.